This course is designed for students who seek a deep understanding of the theoretical and practical aspects of numerical methods. The course will cover advanced topics in numerical analysis, focusing on the development, analysis, and implementation of numerical algorithms for solving complex mathematical problems. Emphasis will be placed on the rigorous mathematical foundations of numerical methods, including convergence analysis, stability, and error estimation.

CILO-1: Develop a thorough understanding of the error and stability analysis of numerical methods for solving differential equations to construct numerical methods for real-world problems with accuracy and stability guarantees. CILO-2: Implement and evaluate numerical algorithms using scientific software. CILO-3: Apply advanced numerical techniques to conduct research independently. CILO-4: Disseminate related research results effectively to diverse audiences. CILO-5: Apply numerical analysis in various scientific and engineering domains.